Analysis of covariance structures

A general method is presented for estimating variance components when the experimental design has one random way of classification and a possibly unbalanced fixed classification. The procedure operates on a sample covariance matrix in which the fixed classes play the role of variables and the random classes correspond to observations. Cases are considered which assume (i) homogeneous and (ii) nonhomogeneous error variance, and (iii) arbitrary scale factors in the measurements and homogeneous error variance. The results include maximum-likelihood estimations of the variance components and scale factors, likelihood-ratio tests of the goodness-of-fit of the model assumed for the design, and large-sample variances and covariances of the estimates. Applications to mental test data are presented. In these applications the subjects constitute the random dimension of the design, and a classification of the mental tests according to objective features of format or content constitute the fixed dimensions.Preparation of this paper has been supported in part by NSF Grant GB-939 and U. S. P. H. Grant GM-1286-01. Computer time was donated by the Computation Center, University of Chicago.Now at the University of Chicago.Now at the University of Georgia.     

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.     

Morphophonological influences on the construction of subject-verb agreement

In three experiments, we investigated whether the production of subject-verb number agreement is affected by the phonological realization of grammatical information. Speakers repeated and completed German or Dutch noun phrases along the lines of The position against the demonstrations. We varied the number of the subject noun (position) and the local noun (demonstrations), as well as the number ambiguity of the subject noun's determiner and the case ambiguity of the local noun phrase. Sentence completions more often contained a verb of the wrong number if the subject and the local nouns mismatched in number than if they matched. Experiments 1 and 2, in German, showed a stronger number mismatch effect if the local noun phrase was ambiguous between the nominative and the accusative cases. Experiment 3, in Dutch, showed a stronger mismatch effect if the subject noun's determiner was ambiguous in number. We conclude that morphophonological factors affect the implementation of agreement during grammatical encoding.     

Broken agreement

The subjects and verbs of English sentences agree in number. This superficially simple syntactic operation is regularly implemented by speakers, but occasionally derails in sentences such as The cost of the improvements have not yet been estimated. We examined whether the incidence of such errors was related to the presence of subject-like semantic features in the immediate preverbal nouns, in light of current questions about the semantic versus syntactic nature of sentence subjects and the interactivity of language processing. In three experiments, speakers completed sentence fragments designed to elicit erroneous agreement. We varied the number and animacy of the head noun and the immediate preverbal (local) noun, as well as the amount of material separating the head noun from the verb. The plurality of the local noun phrase had a large and reliable effect on the incidence of agreement errors, but neither its animacy nor its length affected their occurrence. The latter findings suggest, respectively, that the semantic features of sentence subjects are of minimal relevance to the syntactic and morphological processes that implement agreement, and that agreement features are specified at a point in processing where the eventual length of sentential constituents has little effect on syntactic planning. Both results follow naturally from explanations of language production that emphasize the segregation of sentence formulation processes into relatively autonomous components.     

Some attractions of verb agreement

In English, words like scissors are grammatically plural but conceptually singular, while words like suds are both grammatically and conceptually plural. Words like army can be construed plurally, despite being grammatically singular. To explore whether and how congruence between grammatical and conceptual number affected the production of subject-verb number agreement in English, we elicited sentence completions for complex subject noun phrases like The advertisement for the scissors. In these phrases, singular subject nouns were followed by distractor words whose grammatical and conceptual numbers varied. The incidence of plural attraction (the use of plural verbs after plural distractors) increased only when distractors were grammatically plural, and revealed no influence from the distractors' number meanings. Companion experiments in Dutch offered converging support for this account and suggested that similar agreement processes operate in that language. The findings argue for a component of agreement that is sensitive primarily to the grammatical reflections of number. Together with other results, the evidence indicates that the implementation of agreement in languages like English and Dutch involves separable processes of number marking and number morphing, in which number meaning plays different parts.     

Persistent structural priming from language comprehension to language production

To examine the relationship between syntactic processes in language comprehension and language production, we compared structural persistence from sentence primes that speakers heard to persistence from primes that speakers produced. [Bock, J. K., & Griffin, Z. M. (2000). The persistence of structural priming: transient activation or implicit learning? Journal of Experimental Psychology: General, 129, 177-192.] showed that the production of target priming structures increased the probability of spontaneously using the same structures to describe events in subsequent pictures that were semantically unrelated to the primes. These priming effects persisted across as many as ten intervening filler trials. The present studies replicated these results using auditorily presented primes to which participants only listened. The results indicated persistence of priming across all lags, with relative magnitudes of priming as large as those observed by Bock and Griffin. The implication is that structural priming is persistent regardless of the modality in which language structures are experienced, underscoring the power of priming as an implicit learning mechanism.